scholarly journals Convergence of nonlocal geometric flows to anisotropic mean curvature motion

2021 ◽  
Vol 41 (10) ◽  
pp. 4987
Author(s):  
Annalisa Cesaroni ◽  
Valerio Pagliari
Keyword(s):  
Mean Curvature ◽  
Geometric Flows ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
Anisotropic Mean Curvature

scholarly journals APPROXIMATION OF THE ANISOTROPIC MEAN CURVATURE FLOW

2007 ◽  
Vol 17 (06) ◽  
pp. 833-844 ◽  
Author(s):  
ANTONIN CHAMBOLLE ◽  
MATTEO NOVAGA
Keyword(s):  
Mean Curvature ◽  
Variational Approach ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
Anisotropic Mean Curvature ◽  
Anisotropic Case

In this paper, we provide simple proofs of consistency for two well-known algorithms for mean curvature motion, Almgren–Taylor–Wang's1variational approach, and Merriman–Bence–Osher's algorithm.29Our techniques, based on the same notion of strict sub- and superflows, also work in the (smooth) anisotropic case.

The Influence of the Exterior Surface on Grain Boundary Mobility Measurements

2014 ◽  
Vol 95 ◽  
pp. 56-65
Author(s):  
Amy Novick-Cohen ◽  
Anna Zigelman ◽  
Arkady Vilenkin
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Mean Curvature ◽  
Boundary Energy ◽  
Polycrystalline Materials ◽  
Normal Velocity ◽  
Exterior Surface ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
Half Loop

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reducethe overall energy of the microstructure. The evolution of the microstructure is influencedby the motion of the exterior surface since the grain boundaries couple to the exterior surface of the specimen; these effects can be appreciable especially in thin specimens. We model these effects using the classical framework of Mullins, in whichgrain boundaries move by mean curvature motion, Vn =A κ, and the exterior surface evolves by surface diffusion, Vn = -BΔs κ. Here Vn and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δs is the surface Laplacian. A classical way to determine A, the ``reduced mobility," is to make measurements based on the half-loop bicrystalline geometry. In this geometry one of the two grains, which embedded within the other, recedes at a roughly constant rate which can provide an estimate for A. In this note, we report on findings concerning the effects of the exterior surface on grain boundary motion and mobility measurements in the context of the half-loop bicrystalline geometry. We assume that the ratio of grain boundary energy to the exterior surface energy is small, and suitable assumptions are made of the specimen aspect ratio.

A Representation Formula for the Mean Curvature Motion

2001 ◽  
Vol 33 (4) ◽  
pp. 827-846 ◽  
Author(s):  
R. Buckdahn ◽  
P. Cardaliaguet ◽  
M. Quincampoix
Keyword(s):  
Mean Curvature ◽  
Representation Formula ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
The Mean

scholarly journals Kinerja OpenMP pada Pengolahan Citra dengan Model Curvature Motion

2018 ◽  
Vol 3 (1) ◽  
pp. 97
Author(s):  
Hasbi Rabbani ◽  
Putu Harry Gunawan
Keyword(s):  
Finite Difference ◽  
Mean Curvature ◽  
Mean Curvature Motion ◽  
Curvature Motion

<p>Evolusi dari sebuah bentuk geometri meliputi perubahan curvature yang terdapat dalam<br />bentuk tersebut. Perubahan curvature ini tidak lepas dari perpindahan titik-titik pembentuknya<br />dan diformulakan sebagai Mean Curvature Motion (MCM). MCM telah dipelajari secara<br />mendalam untuk menyelesaikan salah satunya kurva Jordan pada pemodelan fisis. Pada jurnal<br />ini, solusi MCM diaproksimasi menggunakan skema finite  difference dan disimulasikan ke<br />dalam paralel OpenMP. Untuk menghitung performansi paralel, dilakukan simulasi sebanyak<br />10 niter berbeda pada thread sejumlah 2, 4, dan 8. Dari simulasi yang telah dilakukan,<br />didapatkan hasil bahwa performa paralel lebih membutuhkan waktu komputasi yang lebih<br />rendah daripada serial. Selain itu, didapat pula rata-rata efisiensi kode paralel menggunakan<br />2 Thread lebih tinggi daripada menggunakan 4 Thread dan 8 Thread. Sebagai contoh pada<br />ukuran niter 50000, kecepatan masing-masing 2, 4, dan 8 Thread adalah 180.422, 156.002,<br />dan 333.243 s, serta efisiensi masing-masing 2, 4, dan 8 Thread adalah 113%, 66%, dan<br />34,8%.</p>

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